static const float lut[256] = {
    0.137931034482759, 0.168468559837728, 0.199006085192698, 0.227436601952595,
    0.250326371127758, 0.269655908893719, 0.286552162316636, 0.301661083446312,
    0.315391464327659, 0.328020341438308, 0.339745155843731, 0.350712168700108,
    0.361033101195623, 0.370795445142334, 0.380069148968103, 0.38891111873282,
    0.397368344863586, 0.405480133038227, 0.413279732971827, 0.420795551702377,
    0.428052073447331, 0.435070567978911, 0.441869643799548, 0.448465685564231,
    0.454873203905191, 0.461105118087503, 0.467172986539967, 0.473087196491489,
    0.478857121200543, 0.484491251265782, 0.489997305029645, 0.495382321984149,
    0.500652742255517, 0.50581447460931,  0.510872954929035, 0.515833196741626,
    0.520699835066138, 0.52547716462762,  0.530169173291951, 0.534779571428476,
    0.539311817787439, 0.543769142382095, 0.548154566786349, 0.552470922194025,
    0.5567208655326,   0.560906893880184, 0.56503135739791,  0.569096470959395,
    0.573104324633273, 0.577056893153355, 0.580956044492706, 0.584803547642573,
    0.588601079683958, 0.592350232228455, 0.596052517295379, 0.599709372684005,
    0.603322166892625, 0.606892203630022, 0.610420725959665, 0.613908920112298,
    0.617357918998608, 0.62076880545015,  0.62414261521363,  0.627480339720985,
    0.630782928655318, 0.634051292330671, 0.637286303901786, 0.640488801418393,
    0.643659589737087, 0.64679944230263,  0.649909102809338, 0.652989286752218,
    0.656040682876615, 0.659063954534329, 0.662059740953413, 0.665028658428248,
    0.667971301435892, 0.670888243684168, 0.673780039096496, 0.676647222738057,
    0.679490311687462, 0.682309805857786, 0.685106188770483, 0.687879928285438,
    0.690631477290126, 0.693361274350635, 0.696069744327085, 0.698757298955773,
    0.701424337400216, 0.704071246773071, 0.706698402630793, 0.70930616944274,
    0.711894901036301, 0.714464941019526, 0.717016623182628, 0.719550271879615,
    0.722066202391245, 0.72456472127039,  0.727046126670848, 0.729510708660545,
    0.731958749520023, 0.734390524027041, 0.736806299728077, 0.739206337197437,
    0.741590890284669, 0.743960206350907, 0.746314526494747, 0.748654085768202,
    0.750979113383275, 0.753289832909632, 0.755586462463827, 0.757869214890541,
    0.760138297936206, 0.762393914415427, 0.764636262370551, 0.76686553522471,
    0.769081921928692, 0.771285607101899, 0.773476771167714, 0.775655590483521,
    0.777822237465641, 0.779976880709428, 0.782119685104739, 0.784250811947004,
    0.786370419044088, 0.788478660819148, 0.790575688409655, 0.792661649762762,
    0.794736689727171, 0.79680095014167,  0.798854569920459, 0.800897685135439,
    0.802930429095561, 0.804952932423388, 0.80696532312897,  0.808967726681158,
    0.810960266076453, 0.812943061905506, 0.814916232417348, 0.816879893581463,
    0.818834159147776, 0.820779140704649, 0.822714947734959, 0.824641687670338,
    0.826559465943655, 0.828468386039784, 0.830368549544759, 0.832260056193354,
    0.834143003915151, 0.836017488879171, 0.837883605537097, 0.839741446665164,
    0.841591103404754, 0.843432665301749, 0.845266220344684, 0.847091855001746,
    0.848909654256666, 0.850719701643533, 0.852522079280583, 0.854316867902982,
    0.856104146894662, 0.857883994319215, 0.859656486949909, 0.861421700298826,
    0.863179708645183, 0.864930585062832, 0.866674401446999, 0.868411228540266,
    0.870141135957823, 0.87186419221203,  0.873580464736299, 0.875290019908316,
    0.876992923072636, 0.878689238562669, 0.880379029722064, 0.882062358925529,
    0.883739287599096, 0.885409876239847, 0.88707418443512,  0.888732270881216,
    0.890384193401619, 0.892030008964739, 0.893669773701208, 0.895303542920722,
    0.896931371128463, 0.898553312041102, 0.900169418602399, 0.901779742998414,
    0.903384336672333, 0.904983250338937, 0.906576533998706, 0.908164236951579,
    0.909746407810381, 0.911323094513921, 0.912894344339776, 0.914460203916766,
    0.916020719237136, 0.917575935668439, 0.919125897965147, 0.920670650279987,
    0.922210236175006, 0.923744698632384, 0.925274080064996, 0.926798422326728,
    0.928317766722556, 0.929832154018398, 0.931341624450739, 0.932846217736039,
    0.934345973079934, 0.935840929186217, 0.937331124265641, 0.938816596044503,
    0.940297381773056, 0.941773518233727, 0.943245041749159, 0.944711988190075,
    0.946174392982977, 0.947632291117671, 0.949085717154637, 0.950534705232238,
    0.951979289073778, 0.95341950199441,  0.954855376907894, 0.956286946333219,
    0.957714242401086, 0.959137296860253, 0.960556141083747, 0.961970806074959,
    0.963381322473596, 0.964787720561529, 0.966190030268511, 0.967588281177783,
    0.968982502531565, 0.970372723236441, 0.97175897186863,  0.973141276679158,
    0.974519665598923, 0.975894166243664, 0.977264805918825, 0.978631611624336,
    0.979994610059289, 0.981353827626528, 0.98270929043715,  0.984061024314923,
    0.98540905480061,  0.986753407156221, 0.988094106369176, 0.989431177156393,
    0.990764643968298, 0.992094530992764, 0.993420862158964, 0.994743661141167,
    0.996062951362455, 0.997378755998369, 0.998691097980501, 1,
};